Oenothera preliminary analyses
Questions we are exploring
Do floral traits vary across populations?
If floral traits vary across populations, are patterns of variation clinal, associated with variation in pollinators, or random?
In this file:
First, I show a number of correlation heat maps for sets of variables overall, and broken out by population.
Second, I provide a list of potential variables/approaches to consider to address the questions above. I then provide the results of most of these analyses, with the caveat that results may shift slightly after we account for response factors in the scent emission data and potentially clean up some erroneous values in the morphology data.
Exploring correlations in the data
Heatmaps of correlations of scent by compound
These visualizations are a bit challenging because there are 40 compounds, so packing the labels onto the plot makes it hard to read. Blank rows in the figures indicate that the population did not have that compound. Here are the compounds that correspond to each number in the figures below:
All data:
Arizona
Zion
Inyo
Logan
Idaho
Heatmaps of correlations of scent by compound group
These are the groupings of the compounds:
| Code | Compounds |
|---|---|
| G.ILE | 2 methylbuyronitrile, nitro-2-methyl butane, cis-2-methylbutyraldoxime, trans-2-methylbutyraldoxime, 2methylbutyl benzoate |
| G.LEU | 3methylbutyronitrile, nitro-3-methyl-butane, cis-3-methylbutyraldoxime, trans-3-methylbutyraldoxime |
| G.VAL | cis-isobutyraldoxime, trans-isobutyraldoxime |
| G.PHE | 2phenylethanol, phenylacetonitrile, nitrophenylethane, phenylacetaldoxime |
| G.OCI | b-myrcene, cis-b-ocimene, trans-b-ocimene, alpha-terpineol |
| G.GER | citronellol, neral, geranial, nerol, geraniol |
| G.LIN | linalool, cis-furanoid-linalool-oxide, trans-furanoid-linalool-oxide, pyran-lin-oxide-ketone, cis-pyranoid-linalool-oxide, trans-pyranoid-linalool-oxide |
| G.CAR | beta-caryophyllene, alpha-humulene, caryophyllene-oxide |
| G.SES | beta-farnesene, Z-E-alpha-farnesene, E-E-alpha-farnesene, farnesene-epoxide, farnesol, nerolidol, isophytol |
Heatmaps of morphology
Heatmaps of morphology & scent by compound group
Floral traits that could vary
| Trait | Approach |
|---|---|
| Floral scent, total emission rate | Linear mixed model analysis across populations of total emission rates in toluene equivalents |
| Floral scent, compound diversity | Linear mixed model analysis of the number of compounds in samples across populations |
| Floral scent, blend composition | Multivariate analysis (e.g. Adonis) plus constrained ordination. Currently using emission rates in toluene equivalents, will ultimately convert this to emission rates adjusted for response factors. |
| This can be done two ways: 1. using emission rates from individual compounds, or 2. using emission rates that are the sums of all compounds produced from a certain biosynthetic cluster/table. | |
| Floral scent, emission rates of key compounds or compound groups | 1. identify what the key compound(s)/compound group(s) are from the constrained ordination. |
| 2. linear mixed model analysis to compare across populations. | |
| Floral morphology | Multivariate analysis (e.g. Adonis) plus constrained ordination, followed by univariate mixed model analyses of key variables. |
| Scent & morphology together | Multivariate analysis (e.g. Adonis) plus constrained ordination |
Total emission rate
This is total emission rate (per g fresh mass) as a function of population, with plant nested within population as a random effect. So this makes use of all measured flowers.
Diagnostics for the model residuals:
Model summary:
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: Comp.Total ~ Population + (1 | Pop_Plant)
## Data: ER_f_mass
##
## REML criterion at convergence: 3472.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.1406 -0.3805 -0.0945 0.2265 3.1638
##
## Random effects:
## Groups Name Variance Std.Dev.
## Pop_Plant (Intercept) 41253189 6423
## Residual 47602593 6899
## Number of obs: 170, groups: Pop_Plant, 77
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 8986.02 3674.54 64.76 2.445 0.0172 *
## PopulationLogan -3062.05 4095.78 65.27 -0.748 0.4574
## PopulationZion 2381.36 4689.80 72.60 0.508 0.6132
## PopulationInyo 7732.06 4292.22 68.50 1.801 0.0760 .
## PopulationArizona 5718.66 3984.84 63.94 1.435 0.1561
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) PpltnL PpltnZ PpltnI
## PopulatnLgn -0.897
## PopulatinZn -0.784 0.703
## PopulatnIny -0.856 0.768 0.671
## PopultnArzn -0.922 0.827 0.723 0.789ANOVA:
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Population 932879544 233219886 4 71.518 4.8993 0.001507 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Estimated marginal means & contrasts across populations:
## $emmeans
## Population emmean SE df lower.CL upper.CL
## Idaho 8986 3685 65.0 1626 16346
## Logan 5924 1814 67.6 2304 9544
## Zion 11367 2917 87.5 5570 17164
## Inyo 16718 2222 80.3 12297 21139
## Arizona 14705 1545 59.7 11614 17796
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## Idaho - Logan 3062 4107 65.5 0.746 0.9448
## Idaho - Zion -2381 4700 72.8 -0.507 0.9865
## Idaho - Inyo -7732 4303 68.7 -1.797 0.3838
## Idaho - Arizona -5719 3996 64.2 -1.431 0.6102
## Logan - Zion -5443 3435 81.4 -1.585 0.5113
## Logan - Inyo -10794 2868 74.9 -3.763 0.0030
## Logan - Arizona -8781 2383 64.2 -3.685 0.0042
## Zion - Inyo -5351 3667 84.8 -1.459 0.5915
## Zion - Arizona -3337 3301 80.4 -1.011 0.8496
## Inyo - Arizona 2013 2706 72.8 0.744 0.9453
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 5 estimates
Interpretation: total scent shows a roughly clinal pattern. Due to the amount of variance, the significant contrasts are that Logan has lower total scent than Inyo or Arizona. Idaho and Zion are intermediate.
Compound diversity
This is the number of compounds detected in a sample as a function of population, with plant nested within population as a random effect. So this makes use of all measured flowers.
Diagnostics for the model residuals:
Model summary:
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: Total ~ Population + (1 | Pop_Plant)
## Data: P_A_totals
##
## REML criterion at convergence: 926
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.55150 -0.49758 0.07761 0.61227 2.09936
##
## Random effects:
## Groups Name Variance Std.Dev.
## Pop_Plant (Intercept) 10.129 3.183
## Residual 9.597 3.098
## Number of obs: 168, groups: Pop_Plant, 77
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 11.776 1.761 64.956 6.686 6.22e-09 ***
## PopulationLogan 1.207 1.968 65.900 0.613 0.5417
## PopulationZion 3.905 2.241 71.508 1.743 0.0857 .
## PopulationInyo 5.803 2.054 68.098 2.825 0.0062 **
## PopulationArizona 4.431 1.911 64.163 2.319 0.0236 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) PpltnL PpltnZ PpltnI
## PopulatnLgn -0.895
## PopulatinZn -0.786 0.704
## PopulatnIny -0.857 0.768 0.674
## PopultnArzn -0.922 0.825 0.725 0.790ANOVA:
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Population 164.99 41.247 4 71.122 4.2979 0.003591 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Estimated marginal means & contrasts across populations:
## $emmeans
## Population emmean SE df lower.CL upper.CL
## Idaho 11.8 1.765 65.6 8.25 15.3
## Logan 13.0 0.879 70.5 11.23 14.7
## Zion 15.7 1.386 84.4 12.92 18.4
## Inyo 17.6 1.058 78.4 15.47 19.7
## Arizona 16.2 0.742 60.5 14.72 17.7
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## Idaho - Logan -1.207 1.97 66.5 -0.612 0.9727
## Idaho - Zion -3.905 2.24 72.2 -1.740 0.4166
## Idaho - Inyo -5.803 2.06 68.8 -2.820 0.0478
## Idaho - Arizona -4.431 1.92 64.8 -2.314 0.1538
## Logan - Zion -2.698 1.64 80.1 -1.644 0.4744
## Logan - Inyo -4.596 1.38 75.1 -3.341 0.0111
## Logan - Arizona -3.224 1.15 66.1 -2.802 0.0503
## Zion - Inyo -1.898 1.74 82.1 -1.089 0.8119
## Zion - Arizona -0.526 1.57 78.3 -0.335 0.9972
## Inyo - Arizona 1.372 1.29 71.9 1.062 0.8253
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 5 estimates
Interpretation: The total number of compounds also shows a clinal pattern. The significant contrasts are that Idaho has fewer compounds than Inyo, Logan has fewer compounds than Inyo, and Logan has marginally fewer compounds than Arizona (P = 0.0497)
Floral scent blend composition, multivariate analyses using individual compounds
Note: these results could change once we are working with emission rates adjusted for response factors
##
## Call:
## adonis(formula = Tol_ord ~ Population, data = Tol_names, permutations = 999, method = "bray")
##
## Permutation: free
## Number of permutations: 999
##
## Terms added sequentially (first to last)
##
## Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
## Population 4 8.679 2.16979 10.888 0.21086 0.001 ***
## Residuals 163 32.482 0.19928 0.78914
## Total 167 41.161 1.00000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1There is a significant effect of population and it explains about 21 % of the variation in scent.
Running a constrained analysis of principle coordinates:
##
## Call:
## capscale(formula = Tol_ord ~ Population, data = Tol_names, distance = "bray")
##
## Partitioning of squared Bray distance:
## Inertia Proportion
## Total 46.821 1.0000
## Constrained 8.862 0.1893
## Unconstrained 37.959 0.8107
##
## Eigenvalues, and their contribution to the squared Bray distance
##
## Importance of components:
## CAP1 CAP2 CAP3 CAP4 MDS1 MDS2 MDS3
## Eigenvalue 6.9019 1.32297 0.384246 0.252877 9.1079 6.0850 3.91502
## Proportion Explained 0.1474 0.02826 0.008207 0.005401 0.1945 0.1300 0.08362
## Cumulative Proportion 0.1474 0.17567 0.183872 0.189273 0.3838 0.5138 0.59738
## MDS4 MDS5 MDS6 MDS7 MDS8 MDS9 MDS10
## Eigenvalue 2.95294 2.18868 1.75820 1.54016 1.21355 1.04530 0.97259
## Proportion Explained 0.06307 0.04675 0.03755 0.03289 0.02592 0.02233 0.02077
## Cumulative Proportion 0.66045 0.70719 0.74474 0.77764 0.80356 0.82588 0.84665
## MDS11 MDS12 MDS13 MDS14 MDS15 MDS16 MDS17
## Eigenvalue 0.78102 0.67758 0.59532 0.53559 0.4731 0.414869 0.357521
## Proportion Explained 0.01668 0.01447 0.01271 0.01144 0.0101 0.008861 0.007636
## Cumulative Proportion 0.86333 0.87781 0.89052 0.90196 0.9121 0.920925 0.928561
## MDS18 MDS19 MDS20 MDS21 MDS22 MDS23
## Eigenvalue 0.354353 0.2809 0.257349 0.244532 0.221743 0.195084
## Proportion Explained 0.007568 0.0060 0.005496 0.005223 0.004736 0.004167
## Cumulative Proportion 0.936129 0.9421 0.947626 0.952849 0.957585 0.961751
## MDS24 MDS25 MDS26 MDS27 MDS28 MDS29
## Eigenvalue 0.170153 0.142909 0.135207 0.124474 0.119278 0.105581
## Proportion Explained 0.003634 0.003052 0.002888 0.002658 0.002548 0.002255
## Cumulative Proportion 0.965385 0.968438 0.971325 0.973984 0.976531 0.978786
## MDS30 MDS31 MDS32 MDS33 MDS34 MDS35
## Eigenvalue 0.099575 0.092666 0.084808 0.070174 0.067182 0.057930
## Proportion Explained 0.002127 0.001979 0.001811 0.001499 0.001435 0.001237
## Cumulative Proportion 0.980913 0.982892 0.984704 0.986202 0.987637 0.988874
## MDS36 MDS37 MDS38 MDS39 MDS40 MDS41
## Eigenvalue 0.05339 0.050786 0.0408325 0.0384256 0.0351385 0.0327479
## Proportion Explained 0.00114 0.001085 0.0008721 0.0008207 0.0007505 0.0006994
## Cumulative Proportion 0.99001 0.991099 0.9919715 0.9927922 0.9935427 0.9942421
## MDS42 MDS43 MDS44 MDS45 MDS46
## Eigenvalue 0.0305022 0.0277473 0.0238504 0.0229640 0.0195549
## Proportion Explained 0.0006515 0.0005926 0.0005094 0.0004905 0.0004177
## Cumulative Proportion 0.9948936 0.9954862 0.9959956 0.9964861 0.9969037
## MDS47 MDS48 MDS49 MDS50 MDS51
## Eigenvalue 0.0188108 0.0160844 0.0152896 0.0132788 0.0131607
## Proportion Explained 0.0004018 0.0003435 0.0003266 0.0002836 0.0002811
## Cumulative Proportion 0.9973055 0.9976490 0.9979755 0.9982592 0.9985402
## MDS52 MDS53 MDS54 MDS55 MDS56
## Eigenvalue 0.0106415 0.0095623 0.0090038 0.0072015 0.0067816
## Proportion Explained 0.0002273 0.0002042 0.0001923 0.0001538 0.0001448
## Cumulative Proportion 0.9987675 0.9989717 0.9991641 0.9993179 0.9994627
## MDS57 MDS58 MDS59 MDS60 MDS61
## Eigenvalue 0.0059235 4.176e-03 3.629e-03 2.946e-03 2.398e-03
## Proportion Explained 0.0001265 8.919e-05 7.751e-05 6.292e-05 5.122e-05
## Cumulative Proportion 0.9995892 9.997e-01 9.998e-01 9.998e-01 9.999e-01
## MDS62 MDS63 MDS64 MDS65 MDS66
## Eigenvalue 2.125e-03 0.0014421 8.689e-04 7.270e-04 5.624e-04
## Proportion Explained 4.539e-05 0.0000308 1.856e-05 1.553e-05 1.201e-05
## Cumulative Proportion 9.999e-01 0.9999462 1.000e+00 1.000e+00 1.000e+00
## MDS67 MDS68
## Eigenvalue 3.410e-04 1.768e-05
## Proportion Explained 7.284e-06 3.777e-07
## Cumulative Proportion 1.000e+00 1.000e+00
##
## Accumulated constrained eigenvalues
## Importance of components:
## CAP1 CAP2 CAP3 CAP4
## Eigenvalue 6.9019 1.3230 0.38425 0.25288
## Proportion Explained 0.7788 0.1493 0.04336 0.02854
## Cumulative Proportion 0.7788 0.9281 0.97146 1.00000
##
## Scaling 2 for species and site scores
## * Species are scaled proportional to eigenvalues
## * Sites are unscaled: weighted dispersion equal on all dimensions
## * General scaling constant of scores:The constrained portion explains about 19% of overall distance. CAP1 explains about 14% and CAP2 expalins about 3% of overall distance.
Plotting the capscale:
Checking to see which compound group(s) are significantly correlated with CAP1 and/or CAP2.
| compounds | cor1 | p1 | cor2 | p2 | sig1 | sig2 |
|---|---|---|---|---|---|---|
| Comp.2methylbutyronitrile | 0.2373 | 0.0053 | -0.5941 | 0.0000 | Yes | Yes |
| Comp.3methylbutyronitrile | 0.4535 | 0.0000 | 0.022 | 0.8373 | Yes | No |
| Comp.b-myrcene | 0.0285 | 0.7719 | -0.1455 | 0.2261 | No | No |
| Comp.cis-b-ocimene | 0.015 | 0.8684 | -0.0455 | 0.6561 | No | No |
| Comp.trans-b-ocimene | 0.0717 | 0.4186 | -0.0202 | 0.8373 | No | No |
| Comp.nitro-2-methyl-butane | 0.3705 | 0.0000 | -0.642 | 0.0000 | Yes | Yes |
| Comp.nitro-3-methyl-butane | 0.4284 | 0.0000 | -0.0122 | 0.8979 | Yes | No |
| Comp.trans-isobutyraldoxime | 0.2897 | 0.0003 | -0.1054 | 0.2900 | Yes | No |
| Comp.cis-isobutyraldoxime | 0.3043 | 0.0003 | -0.1397 | 0.2261 | Yes | No |
| Comp.cis-furanoid-linalool-oxide | -0.0801 | 0.3662 | -0.1166 | 0.2644 | No | No |
| Comp.trans-furanoid-linalool-oxide | -0.1036 | 0.2339 | -0.191 | 0.0754 | No | No |
| Comp.pyran-lin-oxide-ketone | -0.1184 | 0.1806 | -0.175 | 0.1165 | No | No |
| Comp.trans-2-methylbutyraldoxime | 0.3324 | 0.0000 | -0.7002 | 0.0000 | Yes | Yes |
| Comp.trans-3-methylbutyraldoxime | 0.5219 | 0.0000 | -0.1204 | 0.2531 | Yes | No |
| Comp.cis-2-methylbutyraldoxime | 0.3182 | 0.0000 | -0.6877 | 0.0000 | Yes | Yes |
| Comp.cis-3-methylbutyraldoxime | 0.4778 | 0.0000 | -0.0799 | 0.4179 | Yes | No |
| Comp.linalool | 0.674 | 0.0000 | 0.1352 | 0.2261 | Yes | No |
| Comp.beta-caryophyllene | 0.0177 | 0.8627 | 0.1335 | 0.2261 | No | No |
| Comp.beta-farnesene | -0.1192 | 0.1806 | 0.1438 | 0.2261 | No | No |
| Comp.alpha-humulene | 0.0596 | 0.5062 | 0.1203 | 0.2531 | No | No |
| Comp.neral | 0.137 | 0.1277 | -0.0351 | 0.7236 | No | No |
| Comp.alpha-terpineol | 0.428 | 0.0000 | -0.1086 | 0.2805 | Yes | No |
| Comp.Z-E-alpha-farnesene | -0.0946 | 0.2782 | 0.1087 | 0.2805 | No | No |
| Comp.geranial | 0.1588 | 0.0824 | -0.088 | 0.3800 | No | No |
| Comp.cis-pyranoid-linalool-oxide | -0.1145 | 0.1860 | -0.1008 | 0.3099 | No | No |
| Comp.E-E-alpha-farnesene | -0.197 | 0.0247 | 0.1405 | 0.2261 | No | No |
| Comp.citronellol | 0.1219 | 0.1777 | -0.0647 | 0.4908 | No | No |
| Comp.trans-pyranoid-linalool-oxide | -0.1395 | 0.1277 | -0.0823 | 0.4130 | No | No |
| Comp.nerol | 0.1456 | 0.1135 | -0.0664 | 0.4905 | No | No |
| Comp.geraniol | 0.1591 | 0.0824 | -0.0726 | 0.4515 | No | No |
| Comp.2methylbutyl-benzoate | -0.0028 | 0.9715 | -0.2875 | 0.0016 | No | Yes |
| Comp.2phenylethanol | -0.1383 | 0.1277 | 0.109 | 0.2805 | No | No |
| Comp.phenylacetonitrile | -0.2218 | 0.0098 | 0.2402 | 0.0113 | Yes | No |
| Comp.farnesene-epoxide | -0.1577 | 0.0824 | 0.009 | 0.9074 | No | No |
| Comp.caryophyllene-oxide | -0.0383 | 0.6914 | 0.122 | 0.2531 | No | No |
| Comp.nerolidol | -0.2899 | 0.0003 | -0.1223 | 0.2531 | Yes | No |
| Comp.nitrophenylethane | -0.1337 | 0.1342 | 0.1334 | 0.2261 | No | No |
| Comp.phenylacetaldoxime | -0.1165 | 0.1830 | 0.0969 | 0.3255 | No | No |
| Comp.isophytol | 0.3319 | 0.0000 | 0.0422 | 0.6709 | Yes | No |
| Comp.farnesol | -0.2929 | 0.0003 | -0.0757 | 0.4395 | Yes | No |
Correlated with CAP 1: 2methylbutyronitrile (+), 3methylbutyronitrile (+), nitro-2-methyl-butane (+), nitro-3-methyl-butane (+), trans-isobutyraldoxime (+), cis-isobutyraldoxime (+), trans-2-methylbutyraldoxime (+), trans-3-methylbutyraldoxime (+), cis-2-methylbutyraldoxime (+), cis-3-methylbutyraldoxime (+), linalool (+), alpha-terpineol (+), phenylacetonitrile (-), nerolidol (-), isophytol (+), farnesol (-).
Correlated with CAP 2: 2methylbutyronitrile (-), nitro-2-methyl-butane (-), trans-2-methylbutyraldoxime (-), cis-2-methylbutyraldoxime (-), 2methylbutyl-benzoate (-).
Floral scent blend composition, multivariate analyses using groupings by biosynthetic pathway
Note: these results could change once we are working with emission rates adjusted for response factors
These are the groupings of the compounds:
| Code | Compounds |
|---|---|
| G.ILE | 2 methylbuyronitrile, nitro-2-methyl butane, cis-2-methylbutyraldoxime, trans-2-methylbutyraldoxime, 2methylbutyl benzoate |
| G.LEU | 3methylbutyronitrile, nitro-3-methyl-butane, cis-3-methylbutyraldoxime, trans-3-methylbutyraldoxime |
| G.VAL | cis-isobutyraldoxime, trans-isobutyraldoxime |
| G.PHE | 2phenylethanol, phenylacetonitrile, nitrophenylethane, phenylacetaldoxime |
| G.OCI | b-myrcene, cis-b-ocimene, trans-b-ocimene, alpha-terpineol |
| G.GER | citronellol, neral, geranial, nerol, geraniol |
| G.LIN | linalool, cis-furanoid-linalool-oxide, trans-furanoid-linalool-oxide, pyran-lin-oxide-ketone, cis-pyranoid-linalool-oxide, trans-pyranoid-linalool-oxide |
| G.CAR | beta-caryophyllene, alpha-humulene, caryophyllene-oxide |
| G.SES | beta-farnesene, Z-E-alpha-farnesene, E-E-alpha-farnesene, farnesene-epoxide, farnesol, nerolidol, isophytol |
First, running an adonis (comparable to ANOSIM):
##
## Call:
## adonis(formula = ER_f_mass_group_data ~ Population, data = ER_f_mass_groups, permutations = 999, method = "bray")
##
## Permutation: free
## Number of permutations: 999
##
## Terms added sequentially (first to last)
##
## Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
## Population 4 8.296 2.07396 10.989 0.2124 0.001 ***
## Residuals 163 30.762 0.18873 0.7876
## Total 167 39.058 1.0000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Interpretation: The adonis shows a significant effect of population, which explains about 21 % of the variance in scent blend composition.
Running a constrained analysis of principle coordinates:
##
## Call:
## capscale(formula = ER_f_mass_group_data ~ Population, data = ER_f_mass_groups, distance = "bray")
##
## Partitioning of squared Bray distance:
## Inertia Proportion
## Total 44.757 1.0000
## Constrained 8.496 0.1898
## Unconstrained 36.261 0.8102
##
## Eigenvalues, and their contribution to the squared Bray distance
##
## Importance of components:
## CAP1 CAP2 CAP3 CAP4 MDS1 MDS2 MDS3
## Eigenvalue 6.4486 1.38334 0.410119 0.254159 9.3680 6.6820 3.75770
## Proportion Explained 0.1441 0.03091 0.009163 0.005679 0.2093 0.1493 0.08396
## Cumulative Proportion 0.1441 0.17499 0.184150 0.189829 0.3991 0.5484 0.63239
## MDS4 MDS5 MDS6 MDS7 MDS8 MDS9 MDS10
## Eigenvalue 2.57208 2.14636 1.73698 1.23381 1.11262 1.05079 0.73154
## Proportion Explained 0.05747 0.04796 0.03881 0.02757 0.02486 0.02348 0.01634
## Cumulative Proportion 0.68986 0.73781 0.77662 0.80419 0.82905 0.85252 0.86887
## MDS11 MDS12 MDS13 MDS14 MDS15 MDS16 MDS17
## Eigenvalue 0.70426 0.54891 0.49583 0.44799 0.401672 0.34819 0.309869
## Proportion Explained 0.01574 0.01226 0.01108 0.01001 0.008974 0.00778 0.006923
## Cumulative Proportion 0.88460 0.89687 0.90795 0.91796 0.926929 0.93471 0.941632
## MDS18 MDS19 MDS20 MDS21 MDS22 MDS23
## Eigenvalue 0.258755 0.242014 0.207976 0.19288 0.181509 0.159000
## Proportion Explained 0.005781 0.005407 0.004647 0.00431 0.004055 0.003553
## Cumulative Proportion 0.947414 0.952821 0.957468 0.96178 0.965833 0.969385
## MDS24 MDS25 MDS26 MDS27 MDS28 MDS29
## Eigenvalue 0.134483 0.117887 0.112882 0.10428 0.098593 0.076248
## Proportion Explained 0.003005 0.002634 0.002522 0.00233 0.002203 0.001704
## Cumulative Proportion 0.972390 0.975024 0.977546 0.97988 0.982079 0.983782
## MDS30 MDS31 MDS32 MDS33 MDS34 MDS35
## Eigenvalue 0.068703 0.065234 0.060941 0.056455 0.048112 0.045942
## Proportion Explained 0.001535 0.001458 0.001362 0.001261 0.001075 0.001026
## Cumulative Proportion 0.985317 0.986775 0.988136 0.989398 0.990473 0.991499
## MDS36 MDS37 MDS38 MDS39 MDS40
## Eigenvalue 0.0414773 0.0361344 0.0332603 0.0305310 0.0276648
## Proportion Explained 0.0009267 0.0008073 0.0007431 0.0006821 0.0006181
## Cumulative Proportion 0.9924258 0.9932332 0.9939763 0.9946585 0.9952766
## MDS41 MDS42 MDS43 MDS44 MDS45
## Eigenvalue 0.0262145 0.0230895 0.0196186 0.0176009 0.0173172
## Proportion Explained 0.0005857 0.0005159 0.0004383 0.0003933 0.0003869
## Cumulative Proportion 0.9958623 0.9963782 0.9968165 0.9972097 0.9975967
## MDS46 MDS47 MDS48 MDS49 MDS50
## Eigenvalue 0.0133787 0.0124147 0.0114517 0.0106146 0.0092099
## Proportion Explained 0.0002989 0.0002774 0.0002559 0.0002372 0.0002058
## Cumulative Proportion 0.9978956 0.9981729 0.9984288 0.9986660 0.9988717
## MDS51 MDS52 MDS53 MDS54 MDS55
## Eigenvalue 0.0088314 0.0079024 0.0070607 0.0054538 0.0046521
## Proportion Explained 0.0001973 0.0001766 0.0001578 0.0001219 0.0001039
## Cumulative Proportion 0.9990691 0.9992456 0.9994034 0.9995252 0.9996292
## MDS56 MDS57 MDS58 MDS59 MDS60
## Eigenvalue 3.860e-03 3.404e-03 3.102e-03 2.302e-03 1.904e-03
## Proportion Explained 8.624e-05 7.605e-05 6.932e-05 5.143e-05 4.253e-05
## Cumulative Proportion 9.997e-01 9.998e-01 9.999e-01 9.999e-01 1.000e+00
## MDS61 MDS62 MDS63 MDS64
## Eigenvalue 0.0011952 6.184e-04 2.087e-04 2.839e-06
## Proportion Explained 0.0000267 1.382e-05 4.662e-06 6.344e-08
## Cumulative Proportion 0.9999815 1.000e+00 1.000e+00 1.000e+00
##
## Accumulated constrained eigenvalues
## Importance of components:
## CAP1 CAP2 CAP3 CAP4
## Eigenvalue 6.449 1.3833 0.41012 0.25416
## Proportion Explained 0.759 0.1628 0.04827 0.02991
## Cumulative Proportion 0.759 0.9218 0.97009 1.00000
##
## Scaling 2 for species and site scores
## * Species are scaled proportional to eigenvalues
## * Sites are unscaled: weighted dispersion equal on all dimensions
## * General scaling constant of scores:The constrained portion explains about 19% of overall distance. CAP1 explains about 14% and CAP2 expalins about 3% of overall distance.
Plotting the capscale:
Checking to see which compound group(s) are significantly correlated with CAP1 and/or CAP2.
| compounds | cor1 | p1 | cor2 | p2 | sig1 | sig2 |
|---|---|---|---|---|---|---|
| G.ILE | 0.3541 | 0.0000 | -0.6959 | 0.0000 | Yes | Yes |
| G.LEU | 0.515 | 0.0000 | -0.1206 | 0.2685 | Yes | No |
| G.VAL | 0.3264 | 0.0000 | -0.095 | 0.3307 | Yes | No |
| G.PHE | -0.1395 | 0.0918 | 0.0996 | 0.3307 | No | No |
| G.OCI | 0.0848 | 0.3086 | -0.0598 | 0.4410 | No | No |
| G.GER | 0.1594 | 0.0585 | -0.0686 | 0.4410 | No | No |
| G.LIN | 0.6731 | 0.0000 | 0.1379 | 0.2606 | Yes | No |
| G.CAR | 7e-04 | 0.9925 | 0.1325 | 0.2606 | No | No |
| G.SES | -0.203 | 0.0150 | 0.0617 | 0.4410 | No | No |
This table indicates that four compound groups are correlated with CAP1 at P adjusted < 0.01 : ILE, LEU, VAL, and LIN. ILE is the only compound group correlated with CAP2.
Floral scent, univariate analyses of key compounds
Waiting to do this until we have finalized emission rates adjusted for response factors
Floral scent, univariate analyses of key compound groups
Note: these results could change once we are working with emission rates adjusted for response factors. Also will need to check for p-value adjustments for performing mulitple tests (e.g. one test for each compound group).
For each compound group that was correlated with CAP1 and/or CAP2, the emission rate is modeled as a function of population, with plant nested within population as a random effect. This uses data from all measured flowers.
ILE group:
Diagnostics for the model residuals:
Model summary:
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: G.SES ~ Population + (1 | Pop_Plant)
## Data: ER_f_mass_groups
##
## REML criterion at convergence: 2811.6
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -5.3586 -0.1347 -0.0075 0.0032 5.2888
##
## Random effects:
## Groups Name Variance Std.Dev.
## Pop_Plant (Intercept) 2115879 1454.6
## Residual 729697 854.2
## Number of obs: 168, groups: Pop_Plant, 77
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 64.304 714.379 71.112 0.090 0.9285
## PopulationLogan 1363.192 796.445 71.634 1.712 0.0913 .
## PopulationZion 1.073 898.395 73.702 0.001 0.9991
## PopulationInyo 826.893 828.379 72.399 0.998 0.3215
## PopulationArizona -49.431 776.404 70.647 -0.064 0.9494
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) PpltnL PpltnZ PpltnI
## PopulatnLgn -0.897
## PopulatinZn -0.795 0.713
## PopulatnIny -0.862 0.774 0.686
## PopultnArzn -0.920 0.825 0.732 0.793ANOVA:
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Population 8179119 2044780 4 73.677 2.8022 0.03181 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Estimated marginal means & contrasts across populations:
## $emmeans
## Population emmean SE df lower.CL upper.CL
## Idaho 64.3 715 70.0 -1361.2 1490
## Logan 1427.5 352 72.7 725.3 2130
## Zion 65.4 545 77.2 -1019.6 1150
## Inyo 891.2 420 75.1 55.5 1727
## Arizona 14.9 304 67.0 -592.3 622
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## Idaho - Logan -1363.19 797 70.5 -1.711 0.4341
## Idaho - Zion -1.07 899 72.5 -0.001 1.0000
## Idaho - Inyo -826.89 829 71.2 -0.998 0.8555
## Idaho - Arizona 49.43 777 69.5 0.064 1.0000
## Logan - Zion 1362.12 649 75.8 2.099 0.2311
## Logan - Inyo 536.30 548 74.1 0.979 0.8639
## Logan - Arizona 1412.62 465 70.2 3.035 0.0270
## Zion - Inyo -825.82 688 76.4 -1.201 0.7508
## Zion - Arizona 50.50 624 74.7 0.081 1.0000
## Inyo - Arizona 876.32 518 72.2 1.691 0.4458
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 5 estimates
Interpretation: Idaho has higher ILE emissions than Logan. All other contrasts are non-significant.
LEU group:
Diagnostics for the model residuals:
Untransformed residuals look okay, square root transformation (not shown) is comparable and doesn’t affect the results.
Model summary:
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: G.LEU ~ Population + (1 | Pop_Plant)
## Data: ER_f_mass_groups
##
## REML criterion at convergence: 3081.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.2990 -0.3765 -0.0518 0.2097 4.1544
##
## Random effects:
## Groups Name Variance Std.Dev.
## Pop_Plant (Intercept) 5574700 2361
## Residual 5329222 2309
## Number of obs: 168, groups: Pop_Plant, 77
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 2665.86 1308.57 60.73 2.037 0.046 *
## PopulationLogan -2344.83 1461.85 61.65 -1.604 0.114
## PopulationZion -443.34 1664.83 67.20 -0.266 0.791
## PopulationInyo 2224.66 1526.15 63.82 1.458 0.150
## PopulationArizona 777.06 1419.63 59.96 0.547 0.586
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) PpltnL PpltnZ PpltnI
## PopulatnLgn -0.895
## PopulatinZn -0.786 0.704
## PopulatnIny -0.857 0.768 0.674
## PopultnArzn -0.922 0.825 0.725 0.790ANOVA:
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Population 123344474 30836118 4 66.813 5.7862 0.0004641 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Estimated marginal means & contrasts across populations:
## $emmeans
## Population emmean SE df lower.CL upper.CL
## Idaho 2666 1312 65.5 46.9 5285
## Logan 321 653 70.5 -981.5 1624
## Zion 2223 1030 84.5 174.4 4271
## Inyo 4891 786 78.5 3325.1 6456
## Arizona 3443 551 60.5 2340.1 4546
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## Idaho - Logan 2345 1465 66.5 1.600 0.5025
## Idaho - Zion 443 1668 72.2 0.266 0.9989
## Idaho - Inyo -2225 1529 68.7 -1.455 0.5949
## Idaho - Arizona -777 1423 64.8 -0.546 0.9820
## Logan - Zion -1901 1220 80.2 -1.559 0.5278
## Logan - Inyo -4569 1022 75.1 -4.470 0.0003
## Logan - Arizona -3122 855 66.1 -3.652 0.0045
## Zion - Inyo -2668 1296 82.2 -2.059 0.2480
## Zion - Arizona -1220 1168 78.3 -1.045 0.8338
## Inyo - Arizona 1448 960 71.9 1.507 0.5612
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 5 estimates
Interpretation: Inyo and Arizona have higher emission rates of LEU compounds relative to Logan.
VAL group:
Diagnostics for the model residuals:
Untransformed residuals look okay, square root transformation (not shown) is comparable and doesn’t affect the results.
Model summary:
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: G.VAL ~ Population + (1 | Pop_Plant)
## Data: ER_f_mass_groups
##
## REML criterion at convergence: 1335.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.9658 -0.3082 -0.1300 0.0357 4.4262
##
## Random effects:
## Groups Name Variance Std.Dev.
## Pop_Plant (Intercept) 124.9 11.18
## Residual 118.1 10.87
## Number of obs: 168, groups: Pop_Plant, 77
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 11.258 6.184 44.193 1.821 0.0755 .
## PopulationLogan -6.857 6.908 44.972 -0.993 0.3262
## PopulationZion -7.533 7.866 49.700 -0.958 0.3429
## PopulationInyo 4.180 7.211 46.805 0.580 0.5649
## PopulationArizona -4.366 6.709 43.542 -0.651 0.5186
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) PpltnL PpltnZ PpltnI
## PopulatnLgn -0.895
## PopulatinZn -0.786 0.704
## PopulatnIny -0.858 0.768 0.674
## PopultnArzn -0.922 0.825 0.725 0.790ANOVA:
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Population 778.59 194.65 4 49.362 1.6484 0.1771Estimated marginal means & contrasts across populations:
## $emmeans
## Population emmean SE df lower.CL upper.CL
## Idaho 11.26 6.20 65.6 -1.12 23.6
## Logan 4.40 3.09 70.5 -1.75 10.6
## Zion 3.72 4.87 84.3 -5.95 13.4
## Inyo 15.44 3.71 78.4 8.04 22.8
## Arizona 6.89 2.61 60.5 1.68 12.1
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## Idaho - Logan 6.857 6.92 66.6 0.990 0.8588
## Idaho - Zion 7.533 7.88 72.2 0.956 0.8737
## Idaho - Inyo -4.180 7.23 68.8 -0.579 0.9778
## Idaho - Arizona 4.366 6.72 64.8 0.649 0.9662
## Logan - Zion 0.676 5.76 80.1 0.117 1.0000
## Logan - Inyo -11.037 4.83 75.1 -2.285 0.1611
## Logan - Arizona -2.491 4.04 66.2 -0.617 0.9719
## Zion - Inyo -11.713 6.12 82.1 -1.914 0.3185
## Zion - Arizona -3.167 5.52 78.3 -0.574 0.9785
## Inyo - Arizona 8.546 4.54 72.0 1.883 0.3356
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 5 estimates
Interpretation: No differences across populations.
LIN group:
Diagnostics for the model residuals:
Untransformed residuals look okay, square root transformation (not shown) is comparable and doesn’t affect the results.
Model summary:
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: G.LIN ~ Population + (1 | Pop_Plant)
## Data: ER_f_mass_groups
##
## REML criterion at convergence: 3235.6
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.9556 -0.3689 -0.1093 0.2015 3.6416
##
## Random effects:
## Groups Name Variance Std.Dev.
## Pop_Plant (Intercept) 9355167 3059
## Residual 15835932 3979
## Number of obs: 168, groups: Pop_Plant, 77
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 1989.41 1885.59 50.25 1.055 0.29645
## PopulationLogan 657.51 2109.60 51.40 0.312 0.75655
## PopulationZion 3929.64 2425.02 60.03 1.620 0.11038
## PopulationInyo 7418.33 2210.87 54.81 3.355 0.00144 **
## PopulationArizona 6030.42 2043.30 49.54 2.951 0.00482 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) PpltnL PpltnZ PpltnI
## PopulatnLgn -0.894
## PopulatinZn -0.778 0.695
## PopulatnIny -0.853 0.762 0.663
## PopultnArzn -0.923 0.825 0.718 0.787ANOVA:
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Population 509797610 127449403 4 59.245 8.0481 2.985e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Estimated marginal means & contrasts across populations:
## $emmeans
## Population emmean SE df lower.CL upper.CL
## Idaho 1989 1895 60.4 -1800 5779
## Logan 2647 950 67.0 750 4544
## Zion 5919 1527 91.0 2886 8952
## Inyo 9408 1157 81.0 7106 11710
## Arizona 8020 790 55.4 6437 9602
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## Idaho - Logan -658 2120 61.7 -0.310 0.9979
## Idaho - Zion -3930 2433 70.9 -1.615 0.4930
## Idaho - Inyo -7418 2220 65.4 -3.342 0.0117
## Idaho - Arizona -6030 2053 59.6 -2.938 0.0364
## Logan - Zion -3272 1798 83.6 -1.820 0.3694
## Logan - Inyo -6761 1497 75.0 -4.516 0.0002
## Logan - Arizona -5373 1236 61.9 -4.349 0.0005
## Zion - Inyo -3489 1916 87.2 -1.821 0.3682
## Zion - Arizona -2101 1719 81.9 -1.222 0.7386
## Inyo - Arizona 1388 1401 71.6 0.991 0.8586
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 5 estimates
Interpretation: Inyo and Arizona emit more LIN compounds than Idaho or Logan. Zion is intermediate.
For data exploration purposes: These are the analyses of the non-key compound groups, e.g., the groups that were not correlated with CAP1 and/or CAP2.
PHE group:
Diagnostics for the model residuals:
Model summary:
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: G.PHE ~ Population + (1 | Pop_Plant)
## Data: ER_f_mass_groups
##
## REML criterion at convergence: 1256.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -0.729 0.000 0.000 0.000 12.324
##
## Random effects:
## Groups Name Variance Std.Dev.
## Pop_Plant (Intercept) 3.341 1.828
## Residual 115.002 10.724
## Number of obs: 168, groups: Pop_Plant, 77
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) -1.432e-16 3.157e+00 6.397e+01 0.000 1.000
## PopulationLogan 4.313e+00 3.572e+00 6.938e+01 1.207 0.231
## PopulationZion 3.078e-16 4.385e+00 1.008e+02 0.000 1.000
## PopulationInyo 4.586e-16 3.853e+00 8.227e+01 0.000 1.000
## PopulationArizona 3.078e-16 3.425e+00 6.617e+01 0.000 1.000
##
## Correlation of Fixed Effects:
## (Intr) PpltnL PpltnZ PpltnI
## PopulatnLgn -0.884
## PopulatinZn -0.720 0.636
## PopulatnIny -0.819 0.724 0.590
## PopultnArzn -0.922 0.815 0.664 0.755ANOVA:
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Population 561.04 140.26 4 97.092 1.2196 0.3075Estimated marginal means & contrasts across populations:
## $emmeans
## Population emmean SE df lower.CL upper.CL
## Idaho 0.00 3.27 26.2 -6.717 6.72
## Logan 4.31 1.70 46.1 0.894 7.73
## Zion 0.00 3.05 126.7 -6.031 6.03
## Inyo 0.00 2.22 92.9 -4.414 4.41
## Arizona 0.00 1.35 36.4 -2.739 2.74
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## Idaho - Logan -4.31 3.68 29.4 -1.171 0.7676
## Idaho - Zion 0.00 4.47 52.9 0.000 1.0000
## Idaho - Inyo 0.00 3.95 37.8 0.000 1.0000
## Idaho - Arizona 0.00 3.54 27.4 0.000 1.0000
## Logan - Zion 4.31 3.49 101.3 1.236 0.7304
## Logan - Inyo 4.31 2.80 71.4 1.542 0.5393
## Logan - Arizona 4.31 2.17 42.0 1.987 0.2898
## Zion - Inyo 0.00 3.77 114.5 0.000 1.0000
## Zion - Arizona 0.00 3.33 104.5 0.000 1.0000
## Inyo - Arizona 0.00 2.60 71.4 0.000 1.0000
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 5 estimates
Interpretation: Differences can’t really be estimated properly due to the lack of data; these compounds are only produced in Logan.
OCI group:
Diagnostics for the model residuals:
Square-root transformation applied to improve residuals.
Model summary:
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: sqrt(G.OCI) ~ Population + (1 | Pop_Plant)
## Data: ER_f_mass_groups
##
## REML criterion at convergence: 1305.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.6026 -0.2075 -0.0274 0.1715 4.3137
##
## Random effects:
## Groups Name Variance Std.Dev.
## Pop_Plant (Intercept) 324.26 18.007
## Residual 53.52 7.316
## Number of obs: 168, groups: Pop_Plant, 77
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 0.7432 8.4501 72.0670 0.088 0.930
## PopulationLogan 13.9047 9.4123 72.3606 1.477 0.144
## PopulationZion 3.1203 10.5832 73.3258 0.295 0.769
## PopulationInyo 2.0881 9.7782 72.7043 0.214 0.832
## PopulationArizona 19.4294 9.1911 71.8130 2.114 0.038 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) PpltnL PpltnZ PpltnI
## PopulatnLgn -0.898
## PopulatinZn -0.798 0.717
## PopulatnIny -0.864 0.776 0.690
## PopultnArzn -0.919 0.825 0.734 0.795ANOVA:
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Population 662.93 165.73 4 73.351 3.0967 0.0206 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Estimated marginal means & contrasts across populations:
## $emmeans
## Population response SE df lower.CL upper.CL
## Idaho 0.552 12.6 71.1 0.0 310
## Logan 214.563 121.5 72.6 40.7 525
## Zion 14.927 49.2 74.6 0.0 274
## Inyo 8.016 27.9 73.7 0.0 160
## Arizona 406.933 145.9 69.5 168.0 750
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
## Intervals are back-transformed from the sqrt scale
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## Idaho - Logan -13.90 9.41 71.4 -1.477 0.5805
## Idaho - Zion -3.12 10.58 72.4 -0.295 0.9983
## Idaho - Inyo -2.09 9.78 71.8 -0.214 0.9995
## Idaho - Arizona -19.43 9.19 70.9 -2.114 0.2258
## Logan - Zion 10.78 7.60 74.0 1.419 0.6178
## Logan - Inyo 11.82 6.43 73.2 1.836 0.3610
## Logan - Arizona -5.52 5.50 71.3 -1.004 0.8526
## Zion - Inyo 1.03 8.05 74.3 0.128 0.9999
## Zion - Arizona -16.31 7.33 73.3 -2.226 0.1818
## Inyo - Arizona -17.34 6.11 72.2 -2.840 0.0449
##
## Note: contrasts are still on the sqrt scale
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 5 estimates
Interpretation: Arizona has higher emission rates of OCI compounds than Inyo. These compounds are only produced in sizeable volumes in Arizona and Logan (see estimated marginal means above.)
GER group:
Diagnostics for the model residuals:
Model summary:
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: G.GER ~ Population + (1 | Pop_Plant)
## Data: ER_f_mass_groups
##
## REML criterion at convergence: 2374
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.6286 -0.0274 -0.0069 -0.0014 3.4946
##
## Random effects:
## Groups Name Variance Std.Dev.
## Pop_Plant (Intercept) 581244 762.4
## Residual 19085 138.1
## Number of obs: 168, groups: Pop_Plant, 77
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 59.10 344.43 70.70 0.172 0.8643
## PopulationLogan -47.21 383.34 70.77 -0.123 0.9023
## PopulationZion 877.99 429.96 70.95 2.042 0.0449 *
## PopulationInyo -33.78 397.90 70.83 -0.085 0.9326
## PopulationArizona 175.40 374.90 70.65 0.468 0.6413
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) PpltnL PpltnZ PpltnI
## PopulatnLgn -0.899
## PopulatinZn -0.801 0.720
## PopulatnIny -0.866 0.778 0.693
## PopultnArzn -0.919 0.825 0.736 0.795ANOVA:
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Population 199286 49822 4 70.966 2.6105 0.04256 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Estimated marginal means & contrasts across populations:
## $emmeans
## Population emmean SE df lower.CL upper.CL
## Idaho 59.1 344 71.8 -627.5 746
## Logan 11.9 168 72.2 -323.5 347
## Zion 937.1 257 72.5 424.1 1450
## Inyo 25.3 199 72.4 -371.8 422
## Arizona 234.5 148 71.5 -60.6 530
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## Idaho - Logan 47.2 383 71.9 0.123 0.9999
## Idaho - Zion -878.0 430 72.1 -2.042 0.2569
## Idaho - Inyo 33.8 398 72.0 0.085 1.0000
## Idaho - Arizona -175.4 375 71.8 -0.468 0.9900
## Logan - Zion -925.2 307 72.4 -3.009 0.0288
## Logan - Inyo -13.4 261 72.3 -0.052 1.0000
## Logan - Arizona -222.6 224 71.9 -0.993 0.8575
## Zion - Inyo 911.8 325 72.5 2.802 0.0495
## Zion - Arizona 702.6 297 72.3 2.366 0.1365
## Inyo - Arizona -209.2 248 72.0 -0.843 0.9163
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 5 estimates
Interpretation: Zion has higher emission rates of GER compounds than Logan, and Zion is marginally higher than Inyo.
CAR group:
Diagnostics for the model residuals:
Model summary:
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: G.CAR ~ Population + (1 | Pop_Plant)
## Data: ER_f_mass_groups
##
## REML criterion at convergence: 1701.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.5864 -0.1935 -0.0475 -0.0081 4.2689
##
## Random effects:
## Groups Name Variance Std.Dev.
## Pop_Plant (Intercept) 2629.8 51.28
## Residual 751.8 27.42
## Number of obs: 168, groups: Pop_Plant, 77
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 4.554 24.828 63.127 0.183 0.855
## PopulationLogan 37.701 27.673 63.566 1.362 0.178
## PopulationZion 28.918 31.183 65.213 0.927 0.357
## PopulationInyo 28.320 28.772 64.169 0.984 0.329
## PopulationArizona 1.847 26.991 62.739 0.068 0.946
##
## Correlation of Fixed Effects:
## (Intr) PpltnL PpltnZ PpltnI
## PopulatnLgn -0.897
## PopulatinZn -0.796 0.714
## PopulatnIny -0.863 0.774 0.687
## PopultnArzn -0.920 0.825 0.732 0.794ANOVA:
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Population 4686.1 1171.5 4 65.211 1.5583 0.196Estimated marginal means & contrasts across populations:
## $emmeans
## Population emmean SE df lower.CL upper.CL
## Idaho 4.55 24.8 70.4 -44.98 54.1
## Logan 42.25 12.2 72.7 17.89 66.6
## Zion 33.47 18.9 76.4 -4.11 71.1
## Inyo 32.87 14.5 74.7 3.90 61.8
## Arizona 6.40 10.6 67.8 -14.73 27.5
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## Idaho - Logan -37.701 27.7 70.8 -1.362 0.6537
## Idaho - Zion -28.918 31.2 72.5 -0.927 0.8855
## Idaho - Inyo -28.320 28.8 71.4 -0.984 0.8616
## Idaho - Arizona -1.847 27.0 70.0 -0.068 1.0000
## Logan - Zion 8.783 22.5 75.3 0.391 0.9950
## Logan - Inyo 9.381 19.0 73.9 0.494 0.9877
## Logan - Arizona 35.854 16.2 70.6 2.217 0.1855
## Zion - Inyo 0.598 23.8 75.8 0.025 1.0000
## Zion - Arizona 27.071 21.6 74.2 1.251 0.7215
## Inyo - Arizona 26.473 18.0 72.2 1.472 0.5840
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 5 estimates
Interpretation: The populations do not differ in the amount of CAR compounds emitted.
SES group:
Diagnostics for the model residuals:
Untransformed residuals look okay, square root transformation (not shown) is comparable and doesn’t affect the results.
Model summary:
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: G.SES ~ Population + (1 | Pop_Plant)
## Data: ER_f_mass_groups
##
## REML criterion at convergence: 2811.6
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -5.3586 -0.1347 -0.0075 0.0032 5.2888
##
## Random effects:
## Groups Name Variance Std.Dev.
## Pop_Plant (Intercept) 2115879 1454.6
## Residual 729697 854.2
## Number of obs: 168, groups: Pop_Plant, 77
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 64.304 714.379 71.112 0.090 0.9285
## PopulationLogan 1363.192 796.445 71.634 1.712 0.0913 .
## PopulationZion 1.073 898.395 73.702 0.001 0.9991
## PopulationInyo 826.893 828.379 72.399 0.998 0.3215
## PopulationArizona -49.431 776.404 70.647 -0.064 0.9494
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) PpltnL PpltnZ PpltnI
## PopulatnLgn -0.897
## PopulatinZn -0.795 0.713
## PopulatnIny -0.862 0.774 0.686
## PopultnArzn -0.920 0.825 0.732 0.793ANOVA:
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Population 8179119 2044780 4 73.677 2.8022 0.03181 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Estimated marginal means & contrasts across populations:
## $emmeans
## Population emmean SE df lower.CL upper.CL
## Idaho 64.3 715 70.0 -1361.2 1490
## Logan 1427.5 352 72.7 725.3 2130
## Zion 65.4 545 77.2 -1019.6 1150
## Inyo 891.2 420 75.1 55.5 1727
## Arizona 14.9 304 67.0 -592.3 622
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## Idaho - Logan -1363.19 797 70.5 -1.711 0.4341
## Idaho - Zion -1.07 899 72.5 -0.001 1.0000
## Idaho - Inyo -826.89 829 71.2 -0.998 0.8555
## Idaho - Arizona 49.43 777 69.5 0.064 1.0000
## Logan - Zion 1362.12 649 75.8 2.099 0.2311
## Logan - Inyo 536.30 548 74.1 0.979 0.8639
## Logan - Arizona 1412.62 465 70.2 3.035 0.0270
## Zion - Inyo -825.82 688 76.4 -1.201 0.7508
## Zion - Arizona 50.50 624 74.7 0.081 1.0000
## Inyo - Arizona 876.32 518 72.2 1.691 0.4458
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 5 estimates
Interpretation: Logan has higher SES emissions than Arizona. All other contrasts are non-significant.
Floral morphology, multivariate analyses
In order to do multivariate analyses of the morphological variables, I had to drop leaf number and leaf length, because there isn’t enough data.
##
## Call:
## adonis(formula = morph_data ~ Population, data = morph_names, permutations = 999, method = "bray")
##
## Permutation: free
## Number of permutations: 999
##
## Terms added sequentially (first to last)
##
## Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
## Population 4 0.78747 0.196867 23.18 0.44001 0.001 ***
## Residuals 118 1.00219 0.008493 0.55999
## Total 122 1.78966 1.00000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Interpretation: There is a significant effect of Population. It explains about 44 % of the variation in morphology.
Running a constrained analysis of principle coordinates:
##
## Call:
## capscale(formula = morph_data ~ Population, data = morph_names, distance = "bray")
##
## Partitioning of squared Bray distance:
## Inertia Proportion
## Total 2.2714 1.0000
## Constrained 0.8025 0.3533
## Unconstrained 1.4689 0.6467
##
## Eigenvalues, and their contribution to the squared Bray distance
##
## Importance of components:
## CAP1 CAP2 CAP3 CAP4 MDS1 MDS2 MDS3
## Eigenvalue 0.6777 0.10755 0.011998 0.005265 0.5122 0.15690 0.12982
## Proportion Explained 0.2984 0.04735 0.005282 0.002318 0.2255 0.06908 0.05715
## Cumulative Proportion 0.2984 0.34571 0.350996 0.353313 0.5788 0.64790 0.70505
## MDS4 MDS5 MDS6 MDS7 MDS8 MDS9 MDS10
## Eigenvalue 0.10934 0.07594 0.06994 0.05323 0.04606 0.04209 0.03161
## Proportion Explained 0.04814 0.03343 0.03079 0.02344 0.02028 0.01853 0.01392
## Cumulative Proportion 0.75319 0.78662 0.81741 0.84085 0.86113 0.87966 0.89357
## MDS11 MDS12 MDS13 MDS14 MDS15 MDS16
## Eigenvalue 0.02531 0.02302 0.021945 0.019257 0.01669 0.01351
## Proportion Explained 0.01114 0.01014 0.009661 0.008478 0.00735 0.00595
## Cumulative Proportion 0.90472 0.91485 0.924516 0.932994 0.94034 0.94629
## MDS17 MDS18 MDS19 MDS20 MDS21 MDS22
## Eigenvalue 0.013243 0.012687 0.009918 0.009550 0.008693 0.007835
## Proportion Explained 0.005831 0.005585 0.004366 0.004205 0.003827 0.003450
## Cumulative Proportion 0.952125 0.957710 0.962076 0.966281 0.970108 0.973558
## MDS23 MDS24 MDS25 MDS26 MDS27 MDS28
## Eigenvalue 0.007430 0.006422 0.005963 0.004885 0.004453 0.004065
## Proportion Explained 0.003271 0.002827 0.002625 0.002150 0.001960 0.001790
## Cumulative Proportion 0.976829 0.979656 0.982282 0.984432 0.986393 0.988182
## MDS29 MDS30 MDS31 MDS32 MDS33 MDS34
## Eigenvalue 0.003542 0.003202 0.002971 0.002800 0.0021433 0.0020780
## Proportion Explained 0.001559 0.001410 0.001308 0.001233 0.0009436 0.0009149
## Cumulative Proportion 0.989742 0.991152 0.992459 0.993692 0.9946357 0.9955506
## MDS35 MDS36 MDS37 MDS38 MDS39
## Eigenvalue 0.0017288 0.0016244 0.0014017 0.001102 0.0010052
## Proportion Explained 0.0007611 0.0007152 0.0006171 0.000485 0.0004425
## Cumulative Proportion 0.9963117 0.9970269 0.9976440 0.998129 0.9985715
## MDS40 MDS41 MDS42 MDS43 MDS44
## Eigenvalue 0.0009934 0.0006336 0.0005341 0.0004513 0.0003146
## Proportion Explained 0.0004373 0.0002789 0.0002352 0.0001987 0.0001385
## Cumulative Proportion 0.9990088 0.9992877 0.9995229 0.9997216 0.9998601
## MDS45 MDS46 MDS47
## Eigenvalue 2.166e-04 9.861e-05 2.647e-06
## Proportion Explained 9.535e-05 4.341e-05 1.165e-06
## Cumulative Proportion 1.000e+00 1.000e+00 1.000e+00
##
## Accumulated constrained eigenvalues
## Importance of components:
## CAP1 CAP2 CAP3 CAP4
## Eigenvalue 0.6777 0.1076 0.01200 0.005265
## Proportion Explained 0.8445 0.1340 0.01495 0.006560
## Cumulative Proportion 0.8445 0.9785 0.99344 1.000000
##
## Scaling 2 for species and site scores
## * Species are scaled proportional to eigenvalues
## * Sites are unscaled: weighted dispersion equal on all dimensions
## * General scaling constant of scores:The constrained portion explains about 35% of overall distance. CAP1 explains about 29% and CAP2 expalins about 5% of overall distance.
Plotting the capscale:
Checking to see which compound group(s) are significantly correlated with CAP1 and/or CAP2.
| variables | cor1 | p1 | cor2 | p2 | sig1 | sig2 |
|---|---|---|---|---|---|---|
| M.Corolla_D1 | 0.4729 | 0.0000 | -0.3562 | 0.0001 | Yes | Yes |
| M.Corolla_D2 | 0.6348 | 0.0000 | -0.6315 | 0.0000 | Yes | Yes |
| M.Tube_Flare | 0.4552 | 0.0000 | -0.418 | 0.0000 | Yes | Yes |
| M.Stamen_Length | 0.5212 | 0.0000 | -0.5768 | 0.0000 | Yes | Yes |
| M.Style_Length | 0.3368 | 0.0002 | -0.6922 | 0.0000 | Yes | Yes |
| M.Hypanthium_Length | 0.7619 | 0.0000 | 0.1372 | 0.1303 | Yes | No |
| M.Pedicel_Length | -0.4001 | 0.0000 | -0.2798 | 0.0026 | Yes | Yes |
| M.Nectar_Column | 0.8358 | 0.0000 | 0.2068 | 0.0244 | Yes | No |
| M.Percent_Sugar | 0.0515 | 0.5716 | -0.273 | 0.0029 | No | Yes |
From this, all variables except for percent sugar are correlated with CAP1, and all of them are positively correlated except for pedicel length.
All variables except Hypanthium length and nectar column are correlated with CAP2. All of these correlations are negative.
Floral morphology, univariate analyses
Looking at all nine floral morphology variables, as all were correlated with CAP1 and/or CAP2. Each variable is modeled as a function of population, with plant nested within population as a random effect. This uses data from all measured flowers where all variables were measured on the flower.
Corolla D1:
Diagnostics for the model residuals:
Model summary:
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: M.Corolla_D1 ~ Population + (1 | Pop_Plant)
## Data: morph_names
##
## REML criterion at convergence: 870.6
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.34337 -0.33664 0.00126 0.39074 2.27238
##
## Random effects:
## Groups Name Variance Std.Dev.
## Pop_Plant (Intercept) 143.45 11.977
## Residual 24.04 4.903
## Number of obs: 123, groups: Pop_Plant, 67
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 79.377 6.305 57.105 12.589 <2e-16 ***
## PopulationLogan -3.986 7.010 57.211 -0.569 0.572
## PopulationZion 10.214 7.765 58.548 1.315 0.194
## PopulationInyo 10.625 7.228 57.743 1.470 0.147
## PopulationArizona 4.742 6.789 57.052 0.698 0.488
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) PpltnL PpltnZ PpltnI
## PopulatnLgn -0.899
## PopulatinZn -0.812 0.730
## PopulatnIny -0.872 0.785 0.708
## PopultnArzn -0.929 0.835 0.754 0.810ANOVA:
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Population 304.72 76.18 4 58.617 3.1691 0.02001 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Estimated marginal means & contrasts across populations:
## $emmeans
## Population emmean SE df lower.CL upper.CL
## Idaho 79.4 6.31 60.9 66.8 92.0
## Logan 75.4 3.06 61.4 69.3 81.5
## Zion 89.6 4.53 65.2 80.5 98.6
## Inyo 90.0 3.53 63.6 82.9 97.1
## Arizona 84.1 2.52 60.5 79.1 89.2
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## Idaho - Logan 3.986 7.01 61.0 0.568 0.9791
## Idaho - Zion -10.214 7.77 62.3 -1.315 0.6829
## Idaho - Inyo -10.625 7.23 61.5 -1.470 0.5857
## Idaho - Arizona -4.742 6.79 60.8 -0.698 0.9561
## Logan - Zion -14.199 5.47 64.0 -2.595 0.0833
## Logan - Inyo -14.610 4.68 62.6 -3.123 0.0219
## Logan - Arizona -8.728 3.97 61.0 -2.201 0.1934
## Zion - Inyo -0.411 5.75 64.6 -0.072 1.0000
## Zion - Arizona 5.472 5.18 64.0 1.055 0.8284
## Inyo - Arizona 5.883 4.34 62.5 1.356 0.6577
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 5 estimates
Interpretation: There is somewhat of a clinal pattern in corolla dimension 1. The only significant contrast is that Logan is smaller than Inyo.
Corolla D2:
Diagnostics for the model residuals:
Model summary:
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: M.Corolla_D2 ~ Population + (1 | Pop_Plant)
## Data: morph_names
##
## REML criterion at convergence: 804.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.59762 -0.47663 -0.00872 0.42545 1.80755
##
## Random effects:
## Groups Name Variance Std.Dev.
## Pop_Plant (Intercept) 40.91 6.396
## Residual 23.18 4.815
## Number of obs: 123, groups: Pop_Plant, 67
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 80.656 3.712 54.347 21.730 < 2e-16 ***
## PopulationLogan -4.659 4.131 54.846 -1.128 0.2643
## PopulationZion 19.789 4.623 58.987 4.281 6.94e-05 ***
## PopulationInyo 9.753 4.277 56.465 2.281 0.0264 *
## PopulationArizona 3.337 3.996 54.364 0.835 0.4073
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) PpltnL PpltnZ PpltnI
## PopulatnLgn -0.898
## PopulatinZn -0.803 0.721
## PopulatnIny -0.868 0.780 0.697
## PopultnArzn -0.929 0.835 0.746 0.806ANOVA:
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Population 1490.9 372.73 4 59.435 16.077 5.645e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Estimated marginal means & contrasts across populations:
## $emmeans
## Population emmean SE df lower.CL upper.CL
## Idaho 80.7 3.72 57.0 73.2 88.1
## Logan 76.0 1.82 59.7 72.4 79.6
## Zion 100.4 2.76 71.0 94.9 105.9
## Inyo 90.4 2.13 66.2 86.2 94.7
## Arizona 84.0 1.48 57.2 81.0 87.0
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## Idaho - Logan 4.66 4.14 57.5 1.126 0.7922
## Idaho - Zion -19.79 4.63 61.7 -4.275 0.0006
## Idaho - Inyo -9.75 4.28 59.2 -2.277 0.1668
## Idaho - Arizona -3.34 4.00 57.1 -0.834 0.9190
## Logan - Zion -24.45 3.30 67.4 -7.406 <.0001
## Logan - Inyo -14.41 2.80 63.4 -5.155 <.0001
## Logan - Arizona -8.00 2.34 58.7 -3.412 0.0099
## Zion - Inyo 10.04 3.48 69.2 2.883 0.0406
## Zion - Arizona 16.45 3.13 67.7 5.257 <.0001
## Inyo - Arizona 6.42 2.59 63.1 2.476 0.1092
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 5 estimates
Interpretation: Zion has a significantly larger corolla dimension 2 relative to all other populations. Inyo and Arizona have the next largest corolla D2, which is larger than Logan but comparable to Idaho.
Tube Flare:
Diagnostics for the model residuals:
Model summary:
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: M.Tube_Flare ~ Population + (1 | Pop_Plant)
## Data: morph_names
##
## REML criterion at convergence: 355.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.9706 -0.5496 -0.0465 0.5309 3.7018
##
## Random effects:
## Groups Name Variance Std.Dev.
## Pop_Plant (Intercept) 0.5962 0.7721
## Residual 0.6491 0.8057
## Number of obs: 123, groups: Pop_Plant, 67
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 7.7413 0.4932 52.0680 15.697 < 2e-16 ***
## PopulationLogan 0.3058 0.5497 53.1611 0.556 0.580323
## PopulationZion 2.2824 0.6215 60.1527 3.672 0.000513 ***
## PopulationInyo 1.3201 0.5714 55.8579 2.310 0.024600 *
## PopulationArizona 0.7952 0.5310 52.3507 1.497 0.140307
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) PpltnL PpltnZ PpltnI
## PopulatnLgn -0.897
## PopulatinZn -0.793 0.712
## PopulatnIny -0.863 0.774 0.685
## PopultnArzn -0.929 0.833 0.737 0.801ANOVA:
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Population 16.246 4.0615 4 61.203 6.2566 0.0002746 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Estimated marginal means & contrasts across populations:
## $emmeans
## Population emmean SE df lower.CL upper.CL
## Idaho 7.74 0.495 51.7 6.75 8.74
## Logan 8.05 0.244 57.5 7.56 8.53
## Zion 10.02 0.379 76.3 9.27 10.78
## Inyo 9.06 0.289 68.2 8.48 9.64
## Arizona 8.54 0.197 53.8 8.14 8.93
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## Idaho - Logan -0.306 0.552 52.8 -0.554 0.9810
## Idaho - Zion -2.282 0.624 59.8 -3.660 0.0047
## Idaho - Inyo -1.320 0.574 55.5 -2.301 0.1599
## Idaho - Arizona -0.795 0.533 52.0 -1.491 0.5729
## Logan - Zion -1.977 0.450 70.3 -4.390 0.0004
## Logan - Inyo -1.014 0.378 63.6 -2.683 0.0678
## Logan - Arizona -0.489 0.314 56.0 -1.561 0.5283
## Zion - Inyo 0.962 0.476 73.2 2.020 0.2671
## Zion - Arizona 1.487 0.427 70.9 3.482 0.0074
## Inyo - Arizona 0.525 0.350 63.2 1.499 0.5670
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 5 estimates
Interpretation: Zion is equal to Inyo, but greater than Arizona, Logan, and Idaho. Inyo is equal to Arizona and Idaho, and marginally larger than Logan. Idaho, Logan, and Arizona are equivalent.
Stamen Length:
Diagnostics for the model residuals:
Model summary:
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: M.Stamen_Length ~ Population + (1 | Pop_Plant)
## Data: morph_names
##
## REML criterion at convergence: 648.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.47049 -0.43019 0.00874 0.43536 3.02728
##
## Random effects:
## Groups Name Variance Std.Dev.
## Pop_Plant (Intercept) 7.728 2.780
## Residual 7.479 2.735
## Number of obs: 123, groups: Pop_Plant, 67
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 27.2072 1.7404 53.2262 15.633 < 2e-16 ***
## PopulationLogan -3.3777 1.9393 54.1841 -1.742 0.0872 .
## PopulationZion 10.9699 2.1878 60.5919 5.014 4.94e-06 ***
## PopulationInyo 4.1889 2.0142 56.6639 2.080 0.0421 *
## PopulationArizona -0.4901 1.8739 53.4406 -0.262 0.7947
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) PpltnL PpltnZ PpltnI
## PopulatnLgn -0.897
## PopulatinZn -0.795 0.714
## PopulatnIny -0.864 0.775 0.687
## PopultnArzn -0.929 0.833 0.739 0.802ANOVA:
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Population 729.05 182.26 4 61.505 24.371 4.109e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Estimated marginal means & contrasts across populations:
## $emmeans
## Population emmean SE df lower.CL upper.CL
## Idaho 27.2 1.747 52.9 23.7 30.7
## Logan 23.8 0.857 58.0 22.1 25.5
## Zion 38.2 1.327 75.2 35.5 40.8
## Inyo 31.4 1.015 67.8 29.4 33.4
## Arizona 26.7 0.696 54.5 25.3 28.1
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## Idaho - Logan 3.38 1.95 53.8 1.736 0.4215
## Idaho - Zion -10.97 2.19 60.2 -5.000 0.0001
## Idaho - Inyo -4.19 2.02 56.3 -2.073 0.2461
## Idaho - Arizona 0.49 1.88 53.1 0.261 0.9990
## Logan - Zion -14.35 1.58 69.8 -9.081 <.0001
## Logan - Inyo -7.57 1.33 63.5 -5.693 <.0001
## Logan - Arizona -2.89 1.10 56.6 -2.614 0.0812
## Zion - Inyo 6.78 1.67 72.4 4.058 0.0011
## Zion - Arizona 11.46 1.50 70.3 7.647 <.0001
## Inyo - Arizona 4.68 1.23 63.2 3.800 0.0029
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 5 estimates
Interpretation: Zion has longer stamens then all other populations. Inyo has longer stamens than Logan and Arizona, and comparable stamens to Idaho. Idaho, Logan, and Arizona all have comparable stamens.
Style Length:
Diagnostics for the model residuals:
Model summary:
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: M.Style_Length ~ Population + (1 | Pop_Plant)
## Data: morph_names
##
## REML criterion at convergence: 718
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.19257 -0.43689 -0.04113 0.42192 2.99925
##
## Random effects:
## Groups Name Variance Std.Dev.
## Pop_Plant (Intercept) 14.40 3.795
## Residual 13.22 3.636
## Number of obs: 123, groups: Pop_Plant, 67
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 29.579 2.356 49.112 12.556 < 2e-16 ***
## PopulationLogan -3.966 2.625 49.996 -1.511 0.13706
## PopulationZion 9.650 2.958 56.092 3.262 0.00188 **
## PopulationInyo 3.561 2.725 52.347 1.307 0.19701
## PopulationArizona -2.757 2.537 49.295 -1.087 0.28236
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) PpltnL PpltnZ PpltnI
## PopulatnLgn -0.898
## PopulatinZn -0.796 0.715
## PopulatnIny -0.865 0.776 0.688
## PopultnArzn -0.929 0.834 0.740 0.803ANOVA:
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Population 736.85 184.21 4 56.945 13.93 5.509e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Estimated marginal means & contrasts across populations:
## $emmeans
## Population emmean SE df lower.CL upper.CL
## Idaho 29.6 2.364 53.4 24.8 34.3
## Logan 25.6 1.160 58.2 23.3 27.9
## Zion 39.2 1.791 74.8 35.7 42.8
## Inyo 33.1 1.372 67.6 30.4 35.9
## Arizona 26.8 0.942 54.8 24.9 28.7
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## Idaho - Logan 3.97 2.63 54.3 1.506 0.5631
## Idaho - Zion -9.65 2.97 60.4 -3.254 0.0155
## Idaho - Inyo -3.56 2.73 56.7 -1.303 0.6906
## Idaho - Arizona 2.76 2.55 53.6 1.083 0.8143
## Logan - Zion -13.62 2.13 69.5 -6.382 <.0001
## Logan - Inyo -7.53 1.80 63.5 -4.191 0.0008
## Logan - Arizona -1.21 1.49 56.8 -0.809 0.9267
## Zion - Inyo 6.09 2.26 72.1 2.699 0.0639
## Zion - Arizona 12.41 2.02 70.0 6.131 <.0001
## Inyo - Arizona 6.32 1.66 63.2 3.797 0.0030
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 5 estimates
Interpretation: Zion has longer styles then all other populations except Inyo. Inyo has longer stamens than Logan and Arizona, and comparable styles to Idaho. Idaho, Logan, and Arizona all have comparable styles.
Hypanthium Length:
Diagnostics for the model residuals:
It looks like there is one outlier: rm2-28 (Arizona) the fifth flower, measured on 6/19. It has a length of 36.48, but the other four flowers from the plant all have lengths over 100. I suspect that the 100 digit may have been dropped from this measurement. Can we either resolve this from the paper datasheet or remove this outlier?
Model summary:
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: M.Hypanthium_Length ~ Population + (1 | Pop_Plant)
## Data: morph_names
##
## REML criterion at convergence: 1014.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -6.0771 -0.4220 0.0368 0.3934 2.0305
##
## Random effects:
## Groups Name Variance Std.Dev.
## Pop_Plant (Intercept) 29.81 5.46
## Residual 253.87 15.93
## Number of obs: 123, groups: Pop_Plant, 67
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 91.1503 6.0528 27.8283 15.059 6.64e-15 ***
## PopulationLogan 0.6978 6.8364 31.7140 0.102 0.91935
## PopulationZion 30.4081 8.1318 48.2264 3.739 0.00049 ***
## PopulationInyo 38.4985 7.2559 37.6151 5.306 5.23e-06 ***
## PopulationArizona 44.3977 6.5574 29.8187 6.771 1.71e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) PpltnL PpltnZ PpltnI
## PopulatnLgn -0.885
## PopulatinZn -0.744 0.659
## PopulatnIny -0.834 0.739 0.621
## PopultnArzn -0.923 0.817 0.687 0.770ANOVA:
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Population 36680 9169.9 4 50.932 36.121 2.666e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Estimated marginal means & contrasts across populations:
## $emmeans
## Population emmean SE df lower.CL upper.CL
## Idaho 91.2 6.25 23.9 78.2 104.1
## Logan 91.8 3.21 47.6 85.4 98.3
## Zion 121.6 5.45 93.8 110.7 132.4
## Inyo 129.6 4.02 74.9 121.6 137.7
## Arizona 135.5 2.55 40.4 130.4 140.7
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## Idaho - Logan -0.698 7.03 27.4 -0.099 1.0000
## Idaho - Zion -30.408 8.29 42.8 -3.667 0.0058
## Idaho - Inyo -38.499 7.43 32.8 -5.179 0.0001
## Idaho - Arizona -44.398 6.75 25.7 -6.574 <.0001
## Logan - Zion -29.710 6.32 80.0 -4.698 0.0001
## Logan - Inyo -37.801 5.15 62.9 -7.341 <.0001
## Logan - Arizona -43.700 4.11 44.7 -10.645 <.0001
## Zion - Inyo -8.090 6.77 87.1 -1.195 0.7544
## Zion - Arizona -13.990 6.02 81.9 -2.325 0.1474
## Inyo - Arizona -5.899 4.77 62.9 -1.238 0.7295
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 5 estimates
Interpretation: Clinal pattern. Idaho and Logan have the same lengths, which are lower than the other three populations. Zion, Inyo, and Arizona are all comparable.
Pedicel length:
Note: there are some potential outliers/zeros values that maybe should be NAs in the dataset right now.
Diagnostics for the model residuals:
Model summary:
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: M.Pedicel_Length ~ Population + (1 | Pop_Plant)
## Data: morph_names
##
## REML criterion at convergence: 782.6
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.2518 -0.4751 -0.1338 0.5967 2.4735
##
## Random effects:
## Groups Name Variance Std.Dev.
## Pop_Plant (Intercept) 24.11 4.910
## Residual 23.23 4.819
## Number of obs: 123, groups: Pop_Plant, 67
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 18.7266 3.0718 45.4450 6.096 2.17e-07 ***
## PopulationLogan -2.1700 3.4229 46.3583 -0.634 0.52921
## PopulationZion -0.1088 3.8612 52.5815 -0.028 0.97762
## PopulationInyo -5.8904 3.5549 48.7453 -1.657 0.10395
## PopulationArizona -9.1322 3.3075 45.6478 -2.761 0.00827 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) PpltnL PpltnZ PpltnI
## PopulatnLgn -0.897
## PopulatinZn -0.796 0.714
## PopulatnIny -0.864 0.775 0.687
## PopultnArzn -0.929 0.833 0.739 0.803ANOVA:
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Population 512.41 128.1 4 53.474 5.5153 0.0008594 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Estimated marginal means & contrasts across populations:
## $emmeans
## Population emmean SE df lower.CL upper.CL
## Idaho 18.73 3.08 52.9 12.54 24.9
## Logan 16.56 1.51 58.0 13.53 19.6
## Zion 18.62 2.34 75.2 13.95 23.3
## Inyo 12.84 1.79 67.8 9.26 16.4
## Arizona 9.59 1.23 54.5 7.13 12.1
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## Idaho - Logan 2.170 3.43 53.9 0.632 0.9692
## Idaho - Zion 0.109 3.87 60.3 0.028 1.0000
## Idaho - Inyo 5.890 3.57 56.4 1.652 0.4717
## Idaho - Arizona 9.132 3.32 53.1 2.751 0.0596
## Logan - Zion -2.061 2.79 69.8 -0.739 0.9465
## Logan - Inyo 3.720 2.35 63.5 1.586 0.5116
## Logan - Arizona 6.962 1.95 56.6 3.571 0.0063
## Zion - Inyo 5.782 2.95 72.4 1.961 0.2956
## Zion - Arizona 9.023 2.64 70.2 3.412 0.0092
## Inyo - Arizona 3.242 2.17 63.2 1.492 0.5715
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 5 estimates
Interpretation: The only significant contrasts are that Logan and Zion have larger pedicel lengths than Arizona.
Nectar column:
Note: there are some potential outliers/zeros values that maybe should be NAs in the dataset right now.
Diagnostics for the model residuals:
Model summary:
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: M.Nectar_Column ~ Population + (1 | Pop_Plant)
## Data: morph_names
##
## REML criterion at convergence: 1279.5
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.8162 -0.5497 -0.0135 0.3524 5.5412
##
## Random effects:
## Groups Name Variance Std.Dev.
## Pop_Plant (Intercept) 289.8 17.02
## Residual 2386.5 48.85
## Number of obs: 123, groups: Pop_Plant, 67
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 39.492 18.647 19.320 2.118 0.04736 *
## PopulationLogan -8.751 21.055 22.271 -0.416 0.68164
## PopulationZion 41.000 25.024 35.784 1.638 0.11010
## PopulationInyo 34.745 22.339 26.922 1.555 0.13154
## PopulationArizona 65.472 20.198 20.819 3.241 0.00394 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) PpltnL PpltnZ PpltnI
## PopulatnLgn -0.886
## PopulatinZn -0.745 0.660
## PopulatnIny -0.835 0.739 0.622
## PopultnArzn -0.923 0.818 0.688 0.771ANOVA:
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Population 93205 23301 4 37.961 9.7636 1.566e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Estimated marginal means & contrasts across populations:
## $emmeans
## Population emmean SE df lower.CL upper.CL
## Idaho 39.5 19.25 24.2 -0.21 79.2
## Logan 30.7 9.88 47.7 10.86 50.6
## Zion 80.5 16.74 93.6 47.25 113.7
## Inyo 74.2 12.37 74.8 49.59 98.9
## Arizona 105.0 7.86 40.6 89.08 120.8
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## Idaho - Logan 8.75 21.6 27.7 0.404 0.9940
## Idaho - Zion -41.00 25.5 43.1 -1.607 0.5010
## Idaho - Inyo -34.74 22.9 33.1 -1.519 0.5581
## Idaho - Arizona -65.47 20.8 26.0 -3.149 0.0305
## Logan - Zion -49.75 19.4 79.9 -2.559 0.0880
## Logan - Inyo -43.50 15.8 63.0 -2.747 0.0582
## Logan - Arizona -74.22 12.6 44.8 -5.877 <.0001
## Zion - Inyo 6.25 20.8 86.9 0.301 0.9982
## Zion - Arizona -24.47 18.5 81.8 -1.323 0.6776
## Inyo - Arizona -30.73 14.7 62.9 -2.096 0.2345
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 5 estimates
Interpretation: The only significant contrast is Logan is lower than Arizona.
Percent sugar:
Note: there are some potential outliers/zeros values that maybe should be NAs in the dataset right now.
Diagnostics for the model residuals:
Model summary:
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: M.Percent_Sugar ~ Population + (1 | Pop_Plant)
## Data: morph_names
##
## REML criterion at convergence: 891.6
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.3383 -0.2860 -0.0027 0.2866 8.4996
##
## Random effects:
## Groups Name Variance Std.Dev.
## Pop_Plant (Intercept) 0.0 0.00
## Residual 98.6 9.93
## Number of obs: 123, groups: Pop_Plant, 67
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 37.600 3.140 118.000 11.974 < 2e-16 ***
## PopulationLogan -14.381 3.597 118.000 -3.998 0.000112 ***
## PopulationZion -9.550 4.441 118.000 -2.151 0.033554 *
## PopulationInyo -10.574 3.879 118.000 -2.726 0.007397 **
## PopulationArizona -13.446 3.429 118.000 -3.922 0.000148 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) PpltnL PpltnZ PpltnI
## PopulatnLgn -0.873
## PopulatinZn -0.707 0.617
## PopulatnIny -0.809 0.707 0.572
## PopultnArzn -0.916 0.799 0.648 0.741
## convergence code: 0
## boundary (singular) fit: see ?isSingularANOVA:
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Population 1825.6 456.39 4 118 4.6286 0.001659 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Estimated marginal means & contrasts across populations:
## $emmeans
## Population emmean SE df lower.CL upper.CL
## Idaho 37.6 3.34 12.7 30.4 44.8
## Logan 23.2 1.78 42.9 19.6 26.8
## Zion 28.1 3.15 101.1 21.8 34.3
## Inyo 27.0 2.29 78.8 22.5 31.6
## Arizona 24.2 1.41 33.7 21.3 27.0
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## Idaho - Logan 14.381 3.79 16.2 3.799 0.0116
## Idaho - Zion 9.550 4.59 31.9 2.081 0.2531
## Idaho - Inyo 10.574 4.05 21.4 2.611 0.1038
## Idaho - Arizona 13.446 3.62 14.6 3.711 0.0158
## Logan - Zion -4.831 3.62 84.8 -1.335 0.6706
## Logan - Inyo -3.808 2.91 63.0 -1.311 0.6857
## Logan - Arizona -0.935 2.27 39.1 -0.411 0.9937
## Zion - Inyo 1.024 3.90 93.6 0.263 0.9989
## Zion - Arizona 3.896 3.45 87.0 1.129 0.7907
## Inyo - Arizona 2.872 2.69 62.7 1.067 0.8224
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 5 estimates
Interpretation: Idaho has higher percent sugar than Logan and Arizona, and marginally higher relative to Inyo.
Multivariate analysis of scent and morphology together
##
## Call:
## adonis(formula = All_data ~ Population, data = All_data_names, permutations = 999, method = "bray")
##
## Permutation: free
## Number of permutations: 999
##
## Terms added sequentially (first to last)
##
## Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
## Population 4 1.0453 0.261329 15.745 0.35189 0.001 ***
## Residuals 116 1.9253 0.016597 0.64811
## Total 120 2.9706 1.00000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Population explains about 35 % of the variation in percent composition of floral scent and in morphology. (As a reminder, population explained about 21 % of variation in the scent only dataset, and about 44 $ of variation in the morphology only dataset.)
Running a constrained analysis of principle coordinates:
##
## Call:
## capscale(formula = All_data ~ Population, data = All_data_names, distance = "bray")
##
## Partitioning of squared Bray distance:
## Inertia Proportion
## Total 3.704 1.0000
## Constrained 1.061 0.2864
## Unconstrained 2.644 0.7136
##
## Eigenvalues, and their contribution to the squared Bray distance
##
## Importance of components:
## CAP1 CAP2 CAP3 CAP4 MDS1 MDS2 MDS3
## Eigenvalue 0.7951 0.15056 0.08507 0.030101 0.5034 0.4648 0.21287
## Proportion Explained 0.2146 0.04064 0.02297 0.008126 0.1359 0.1255 0.05747
## Cumulative Proportion 0.2146 0.25527 0.27824 0.286362 0.4223 0.5477 0.60519
## MDS4 MDS5 MDS6 MDS7 MDS8 MDS9 MDS10
## Eigenvalue 0.18067 0.15667 0.13273 0.12405 0.1045 0.08579 0.08213
## Proportion Explained 0.04877 0.04229 0.03583 0.03349 0.0282 0.02316 0.02217
## Cumulative Proportion 0.65397 0.69626 0.73209 0.76558 0.7938 0.81694 0.83911
## MDS11 MDS12 MDS13 MDS14 MDS15 MDS16 MDS17
## Eigenvalue 0.06590 0.06371 0.04725 0.04650 0.04046 0.034321 0.031504
## Proportion Explained 0.01779 0.01720 0.01276 0.01255 0.01092 0.009265 0.008504
## Cumulative Proportion 0.85690 0.87410 0.88686 0.89941 0.91033 0.919600 0.928104
## MDS18 MDS19 MDS20 MDS21 MDS22 MDS23
## Eigenvalue 0.028040 0.024755 0.023117 0.021404 0.019181 0.014858
## Proportion Explained 0.007569 0.006683 0.006241 0.005778 0.005178 0.004011
## Cumulative Proportion 0.935673 0.942356 0.948596 0.954375 0.959552 0.963564
## MDS24 MDS25 MDS26 MDS27 MDS28 MDS29
## Eigenvalue 0.014464 0.013345 0.011156 0.010981 0.009643 0.009001
## Proportion Explained 0.003905 0.003603 0.003012 0.002964 0.002603 0.002430
## Cumulative Proportion 0.967468 0.971071 0.974082 0.977047 0.979650 0.982079
## MDS30 MDS31 MDS32 MDS33 MDS34 MDS35
## Eigenvalue 0.008403 0.007921 0.007627 0.006737 0.005130 0.004800
## Proportion Explained 0.002268 0.002138 0.002059 0.001819 0.001385 0.001296
## Cumulative Proportion 0.984348 0.986486 0.988545 0.990364 0.991749 0.993045
## MDS36 MDS37 MDS38 MDS39 MDS40 MDS41
## Eigenvalue 0.004281 0.004027 0.0034058 0.0028453 0.0024047 0.0019591
## Proportion Explained 0.001156 0.001087 0.0009194 0.0007681 0.0006492 0.0005289
## Cumulative Proportion 0.994200 0.995287 0.9962068 0.9969749 0.9976240 0.9981529
## MDS42 MDS43 MDS44 MDS45 MDS46
## Eigenvalue 0.0017540 0.0013611 0.0012118 0.0007853 0.0006208
## Proportion Explained 0.0004735 0.0003674 0.0003271 0.0002120 0.0001676
## Cumulative Proportion 0.9986264 0.9989938 0.9993209 0.9995329 0.9997005
## MDS47 MDS48 MDS49
## Eigenvalue 0.0005521 3.558e-04 2.015e-04
## Proportion Explained 0.0001490 9.604e-05 5.439e-05
## Cumulative Proportion 0.9998496 9.999e-01 1.000e+00
##
## Accumulated constrained eigenvalues
## Importance of components:
## CAP1 CAP2 CAP3 CAP4
## Eigenvalue 0.7951 0.1506 0.08507 0.03010
## Proportion Explained 0.7495 0.1419 0.08020 0.02838
## Cumulative Proportion 0.7495 0.8914 0.97162 1.00000
##
## Scaling 2 for species and site scores
## * Species are scaled proportional to eigenvalues
## * Sites are unscaled: weighted dispersion equal on all dimensions
## * General scaling constant of scores:The constrained portion explains about 29% of overall distance. CAP1 explains about 21% and CAP2 expalins about 4% of overall distance.
Plotting the capscale:
Checking to see which compound group(s) are significantly correlated with CAP1 and/or CAP2.
| variables | cor1 | p1 | cor2 | p2 | sig1 | sig2 |
|---|---|---|---|---|---|---|
| M.Corolla_D1 | 0.4468 | 0.0000 | -0.2509 | 0.0199 | Yes | No |
| M.Corolla_D2 | 0.6025 | 0.0000 | -0.3419 | 0.0006 | Yes | Yes |
| M.Tube_Flare | 0.3976 | 0.0000 | -0.3712 | 0.0002 | Yes | Yes |
| M.Stamen_Length | 0.4969 | 0.0000 | -0.3763 | 0.0001 | Yes | Yes |
| M.Style_Length | 0.3052 | 0.0026 | -0.2878 | 0.0059 | Yes | Yes |
| M.Hypanthium_Length | 0.7833 | 0.0000 | 0.1658 | 0.1625 | Yes | No |
| M.Pedicel_Length | -0.4327 | 0.0000 | -0.2143 | 0.0505 | Yes | No |
| M.Nectar_Column | 0.7893 | 0.0000 | 0.0023 | 0.9875 | Yes | No |
| M.Percent_Sugar | 0.0464 | 0.6702 | -0.4667 | 0.0000 | No | Yes |
| Comp.2methylbutyronitrile | 0.1497 | 0.1401 | -0.5429 | 0.0000 | No | Yes |
| Comp.3methylbutyronitrile | 0.2968 | 0.0032 | -0.0119 | 0.9575 | Yes | No |
| Comp.b-myrcene | -0.1097 | 0.2855 | -0.0919 | 0.4956 | No | No |
| Comp.cis-b-ocimene | -0.1635 | 0.1042 | 0.197 | 0.0792 | No | No |
| Comp.trans-b-ocimene | -0.0255 | 0.7809 | 0.2727 | 0.0097 | No | Yes |
| Comp.nitro-2-methyl-butane | 0.1247 | 0.2196 | -0.4895 | 0.0000 | No | Yes |
| Comp.nitro-3-methyl-butane | 0.1663 | 0.1004 | -0.1297 | 0.2826 | No | No |
| Comp.trans-isobutyraldoxime | 0.0791 | 0.4423 | -0.1217 | 0.3196 | No | No |
| Comp.cis-isobutyraldoxime | 0.0895 | 0.3965 | -0.1546 | 0.2024 | No | No |
| Comp.cis-furanoid-linalool-oxide | -0.218 | 0.0333 | -0.135 | 0.2627 | No | No |
| Comp.trans-furanoid-linalool-oxide | -0.1782 | 0.0792 | -0.1927 | 0.0847 | No | No |
| Comp.pyran-lin-oxide-ketone | -0.2413 | 0.0164 | -0.0922 | 0.4956 | No | No |
| Comp.trans-2-methylbutyraldoxime | -0.0444 | 0.6716 | -0.733 | 0.0000 | No | Yes |
| Comp.trans-3-methylbutyraldoxime | 0.3685 | 0.0002 | -0.3019 | 0.0036 | Yes | Yes |
| Comp.cis-2-methylbutyraldoxime | -0.0268 | 0.7809 | -0.7443 | 0.0000 | No | Yes |
| Comp.cis-3-methylbutyraldoxime | 0.3492 | 0.0004 | -0.2406 | 0.0264 | Yes | No |
| Comp.linalool | 0.2512 | 0.0128 | 0.5655 | 0.0000 | No | Yes |
| Comp.beta-caryophyllene | -0.1906 | 0.0704 | 0.0397 | 0.8450 | No | No |
| Comp.beta-farnesene | -0.2549 | 0.0118 | -0.0309 | 0.8658 | No | No |
| Comp.alpha-humulene | -0.1269 | 0.2160 | 0.0479 | 0.7853 | No | No |
| Comp.neral | 0.2634 | 0.0092 | -0.0285 | 0.8666 | Yes | No |
| Comp.alpha-terpineol | -0.1788 | 0.0792 | -0.0096 | 0.9575 | No | No |
| Comp.Z-E-alpha-farnesene | -0.2982 | 0.0032 | 0.1006 | 0.4571 | Yes | No |
| Comp.geranial | 0.2825 | 0.0048 | -0.0565 | 0.7226 | Yes | No |
| Comp.cis-pyranoid-linalool-oxide | -0.2819 | 0.0048 | -0.1488 | 0.2207 | Yes | No |
| Comp.E-E-alpha-farnesene | -0.3669 | 0.0002 | 0.1409 | 0.2412 | Yes | No |
| Comp.citronellol | 0.1423 | 0.1605 | 0.0655 | 0.6570 | No | No |
| Comp.trans-pyranoid-linalool-oxide | -0.1819 | 0.0792 | -0.2168 | 0.0497 | No | No |
| Comp.nerol | 0.1797 | 0.0792 | 0.0816 | 0.5665 | No | No |
| Comp.geraniol | 0.1878 | 0.0708 | -0.0312 | 0.8658 | No | No |
| Comp.2methylbutyl-benzoate | NA | NA | NA | NA | NA | NA |
| Comp.2phenylethanol | -0.1663 | 0.1004 | -0.0332 | 0.8658 | No | No |
| Comp.phenylacetonitrile | -0.2863 | 0.0046 | 0.0778 | 0.5822 | Yes | No |
| Comp.farnesene-epoxide | -0.1894 | 0.0704 | 0.1447 | 0.2318 | No | No |
| Comp.caryophyllene-oxide | -0.078 | 0.4423 | -0.0014 | 0.9875 | No | No |
| Comp.nerolidol | -0.2493 | 0.0130 | -0.0754 | 0.5855 | No | No |
| Comp.nitrophenylethane | -0.0798 | 0.4423 | -0.0176 | 0.9487 | No | No |
| Comp.phenylacetaldoxime | NA | NA | NA | NA | NA | NA |
| Comp.isophytol | -0.0335 | 0.7466 | 0.221 | 0.0465 | No | No |
| Comp.farnesol | -0.3887 | 0.0001 | 0.0104 | 0.9575 | Yes | No |
Correlated with CAP 1: all morphological variables except percent sugar (all + except Hypanthium length), 3methylbutyronitrile (+), trans-3-methylbutyraldoxime (+), cis-3-methylbutyraldoxime (+), neral (+), Z-E-alpha-farnesene (-), geranial (+), cis-pyranoid-linalool-oxide (-), E-E-alpha-farnesene (-), phenylacetonitrile (-), farnesol (-)
Correlated with CAP 2: corolla D2 (-), Tube flare (-), stamen length (-), style length (-), percent sugar (-), 2methylbutyronitrile (+), trans-b-ocimene (+), nitro-2-methyl-butane (-), trans-2-methylbutyraldoxime (-), trans-3-methylbutyraldoxime (-), cis-2-methylbutyraldoxime (-), linalool (+).